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**2-5 Absolute Value Functions and Graphs**

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**Vertex Maximum or minimum of the graph**

For the equation, the vertex is at

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**Identify the vertex for each function**

1. f(x) = | 2x – 5 | 2. f(x) = | 3x + 6 | 3. f(x) = - |x + 1 | - 2

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**Graphing absolute value functions by making a table**

Find the vertex Make a table of values (at least 5!) Graph the function.

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**Find several ordered pairs for each function.**

Graph and on the same coordinate plane. Determine the similarities and differences in the two graphs. Find several ordered pairs for each function. x | x – 3 | 3 1 2 4 5 x | x + 2 | –4 2 –3 1 –2 –1 3 Example 6-3a

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**Graph the points and connect them.**

Answer: The domain of both graphs is all real numbers. The range of both graphs is The graphs have the same shape, but different x-intercepts. The graph of g (x) is the graph of f (x) translated left 5 units. Example 6-3b

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Graph y = | x – 3 | + 3 X Y

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Graph y = | 2x + 1 | X Y

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**X Y The recommended dietary allowance**

for vitamin C is 2 micrograms per day. Write an absolute value function for the difference Between the number of micrograms of Vit C you ate today x and the recommended amount. X Y

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Graph X Y

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Graph y = | -x – 5 | X Y

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Graph y = | -3x | X Y

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6.7 Graphing Absolute Value Equations. Vertical Translations Below are the graphs of y = | x | and y = | x | + 2. Describe how the graphs are the same.

6.7 Graphing Absolute Value Equations. Vertical Translations Below are the graphs of y = | x | and y = | x | + 2. Describe how the graphs are the same.

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